Inclusive approaches to teaching and learning mathematics

This chapter explores the role of mentors in supporting pre-service teachers to include all children in mathematics teaching, no matter what their individual needs.

Promoting mother–infant book sharing and infant attention and language development in an impoverished South African population: a pilot study

The low rates of child literacy in South Africa are cause for considerable concern. Research from the developed world shows that parental sharing of picture books with infants and young children is beneficial for child language and cognitive development, as well as literacy skills. We conducted a pilot study to examine whether such benefits might extend to an impoverished community in South Africa, by evaluating the impact of training mothers in book sharing with their 14–18 month old infants. Seventeen mothers received book sharing training; and 13 mothers did not, but instead received a comparison training in toy play. We assessed the mothers’ behavior during both book sharing and toy play before and after training, and we also assessed infant attention and language. Mothers receiving book sharing training engaged well with it, and they also benefited from it; thus, compared to the comparison group mothers, they became more sensitive, more facilitating, and more elaborative with their infants during book sharing, and they also became more sensitive to their infants during toy play. In addition, infants whose mothers received the book sharing training showed greater benefits than the comparison group infants in both their attention and language. Training in book sharing for families living in conditions of marked socio-economic adversity in South Africa has the potential to be of considerable benefit to child developmental progress. A large scale controlled trial is required to confirm this.

Competing priorities: Singapore teachers’ perspectives on critical literacy

This paper explores a group of Singaporean English language teachers’ knowledge and beliefs about critical literacy as well as their perspectives on how best to teach literacy and critical literacy in Singapore schools. A face-to-face survey was conducted among 58 English language teachers by using open-ended questions. The survey covered various topics related to literacy instruction including text decoding, meaning construction, and critical analysis of texts. The participating teachers believed strongly that reading and writing are transactional and interactional practices. However, they were less certain in their beliefs about teaching critical literacy including the critical, analytical and evaluative aspects of text reading. Some teachers saw a conflict between using time on teaching critical literacy and preparing students to pass their exams. As critical literacy is not a requirement at exams, they found it difficult to justify using time teaching it. The results suggest that the teachers’ belief systems are strongly influenced by the broad macrostructure of the educational system in Singapore and their own educational experiences.

Disambiguating with Bourdieu: unravelling policy from practice in the teaching of children with English as an additional language

This article explores the use of Bourdieusian analysis for examining how policy and practice interact in the teaching of English and therefore in the development of children’s language and literacy; in particular how Bourdieusian analysis uncovers the ways in which teachers’ practice has been influenced unconsciously by centralised shaping of the curriculum for English in England while the pupil demographic in schools has become more linguistically diverse. Data were collected from interviews with both newly qualified and very experienced primary school (pupil ages 5 – 11) teachers, whose pedagogical norms for the teaching of English were challenged by the arrival of non-English speakers in their classrooms. The discussion highlights how the use of Bourdieusian constructs of field, habitus and capital can disambiguate teachers’ practical classroom decisions from the influences of policy expectations.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Spacelike Surfaces in L(4) with Degenerate Gauss Map

In this paper we study and present a complete classification of spacelike surfaces with degenerate Gauss map in the Lorentz-Minkowski space L(4).

Curvature Estimates for Submanifolds in Warped Products

We give estimates of the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.

NAVET's Boxes - an Evaluation of the Post-Visit Loan Service at a Science Centre in Borås

Many pedagogues believe science centres to be a good complement to the more formal school teaching. For a visit to a science centre to be as educational as possible, there is a need for pre-visit information of some sort, a guided visit, and post-visit work. Many science centres offer loan services of different kinds. At Navet, a science centre in Borås, teachers can borrow boxes with experiments connected to the different themes they provide. The experiments are supposed to be a continuation of the visit and help settle the knowledge gained during the visit. This thesis is an evaluation of how the boxes function in the schools, and what the teachers think of them. The study was conducted through questionnaires and interviews with both teachers and the staff at Navet. The results of the study are very positive. Many teachers have been involved with Navet from the very beginning and they see a visit to Navet as an integrated part of their teaching. Some boxes work better than others and some might need clearer information, but overall the teachers see the boxes as timesavers, as a way to vary their teaching more easily, and as a help for teachers not specialized in mathematics and science.

Upper secondary school students' gendered conceptions about mathematics

This study explores Swedish Natural Science students' conceptions about gender and mathematics. I conducted and compared the results from two questionnaires. The first questionnaire revealed a view of rather traditional feminities and masulinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between the traits the students ascribed as gender different and the traits they ascribed to themselves.

Letters, authority and secrecy : The case of Karagwe in Tanzania

This paper aims to show how letters, as a genre of literacy, are used in Karagwe in Tanzania, in relation to authority and secrecy. It is shown that literacy, in the form of letters, plays an important role in the negotiation of authority. Authorities as well as ordinary people use letters according to official norms to claim or manifest authority, while grassroots forms of literacy, dominated forms, are used to resist authorities. Through secret messages and letters people find opportunities to resist that are less dangerous than open rebellion, although the effects may be limited because of the secrecy. It is also shown how children are socialized into this pattern of secrecies through literacy as they are used as messengers. When delivering secret letters and messages, they may be said to exercise a passive voice through literacy.

PANA V : Evaluation of a Literacy Project

PANA V Evaluation of a Literacy ProjectSUMMARY AND CONCLUSIONSThis evaluation set out to explore the impact of the literacy work carried out through PANA V. It focussed on clarifying effects such as empowerment and poverty reduction in relation to the civil society. Two specific objectives were to evaluate the methodological approach and the didactic materials and to evaluate the sustainability of the project.Although the focus of the evaluation has been PANA V, the project has been evaluated in its context, as one in a series of five projects located in Rwanda ten years after the war and genocide. The conclusion will consider future plans in this field.The evaluator has striven to create a holistic picture of the effects of the project, although the given time for the evaluation was short. Only three weeks were spent in the field study and only ten days in the actual field. Although there were some organisational and logistic problems, as is common when carrying out a study like this in a poor country, many literacy sites were visited and quite many participators were interviewed. The overall impression from the study is overwhelmingly positive. So many people commit themselves in this task of teaching Rwandans reading, writing and numeracy. Despite harsh conditions learners strive to learn and group leaders devote themselves to the task. Many leaders on different levels try their very best to manage their difficult and demanding task. The main objective was to explore the impact of the project on poverty reduction, particularly on empowerment and strategies for everyday life. Women were to be regarded particularly. From the results it is clear that the project has a strong, positive impact both on poverty reduction and empowerment of marginalised groups. Among those who have benefited from the alphabetisation are mainly women. Unfortunately, when it comes to leaders in PANA, who may also be said to have benefited from the project, only a small minority is women. This is something that is recommended that it be reconsidered inside the organisation. As a majority of the targeted learners are women, and as the economic and social situation of women in Rwanda is generally weak, this is a question that I recommend the Pentesostal church and ADEPR to look particularly into. With many women being single breadwinners of their households, it is important that also women get access to positions that may bring benefits of different kind.It is also clear that the project has positive effects for the civil society. In the present situation in Rwanda, during the process of reconciliation and rapid progress, basic education for the poor majority is a democratic issue. In a country with a plethora of internet-cafés in the capital and a small minority that use cars and mobile-telephones to communicate nation-wide, it is of outmost importance that the majority acquires basic education, of which literacy is a central part. To strengthen the civil society in Rwanda literacy is important. One central issue is then that Rwanda develops toward becoming a country where literacy is used for the benefit of the citizens and it is a democratic issue that all citizens get an opportunity to participate. Crucial for this is that strong efforts are put into primary schools nation-wide. Literacy projects for adults, like PANA, may only complement these efforts, but they constitute important and necessary complements. Other relevant ways to promote literacy are campaigns in Radio and TV and through cultural events such as festivals, music and theatre. News papers, magazines and books are natural parts of such campaigns as well as adult education. As stated under the results not much can be said about the didactics in this evaluation. On the whole the methodology and the materials fill their function well and receive a high reputation. As people learn to read and write under very simple conditions, obviously the approach is appropriate. A few suggestions may be given from the study:•Focus groups leaders’ attention on clearness, that they show very clearly what is to be read. Good structuring is probably of great importance for many learners.•Make clear what is tested in the tests and consider the possibility to use a holistic test that would be more congruent with the methodology. The possibility to use only one grade, pass, would enable a more practical test, such as reading a short, relevant text, writing something relevant and solving practical mathematic problems. Avoid tests that demand school knowledge.•Avoid using methaphors such as “fight against illiteracy” and connections between illiteracy/literacy and darkness/light. It is not true that illiteracy causes bad things and that literacy only brings good. •Be prepared that it may be more difficult in the future to achieve the goals as it may be the case that the early learners where the ones who achieved easily. The goal of “literacy in six month” in PANA will probably hold only for some learners but also those who do not manage in six months need literacy skills.A third objective was to secure sustainability. As for sustainability of the project in itself, and of the literacy process, the main conclusion is that there is a good potential. The commitment and devotedness among many involved in PANA proves good. One weakness is individual leaders in ADEPR who do not see this as an important task for the Pentecostal church in Rwanda. Other weaknesses are the unwillingness to mention explicitly the wish, for example among group leaders, to get some kind of incentive and the fear of loosing believers by cooperation with other organisations. A higher degree of transparency in this issue would probably solve some irritations and tensions.As for the sustainability of the literacy skills much may be done to improve. The acquired skills seem to be comparably relevant. The level achieved, and the level tested, may be defined as basic literacy skills, consisting of basic reading, writing and numeracy skills. However, these skills are very restricted and there is a high risk that the skills will decline, which means that there is a high risk that people will forget how to read and write because of lack of exercising. From these conclusions a few suggestions for future development will be given.

Globos e mapas ao alcance das mãos : ensino de matemática numa perspectiva de alfabetização funcional na EJA

The following dissertation has as its main advantage the privilege of visualizing the literacy processes through the angle of the functional perspective, which does not see the literary process as a practice solely based on the decoding of alphabetical codes, and then allows for the opening of ample spaces for the allocation of mathematical skills in the realms of the functional literacy. The main object of this study was to investigate which are the contributions that a sequence of activities and of methodologies developed for the teaching of Geometry could provide for a part of the functional literacy process in mathematics of youngsters and adults of EJA, corresponding to the acquisition or to the improvement of skills related to the orientation capacity. The focus of the analyses consisted in the practice of these activities with the young and adult students of an EJA class belonging to a municipal public school of Natal/RN. The legacies of Paulo Freire about the redimensioning of the role of the teacher, of the students, of the knowledge and of their connections within the teaching-learning process, prevailed in the actions of the methodology implemented in the classroom and, especially, in the establishing of dialogic connections with the students, which directed all the observations and analyses regarding the collected information. The results indicated that the composition of articulations between the teaching of mathematics and the exploration of maps and the earth globe enabled the creation of multidisciplinary learning environments and situations, where we could observe, gradually, the development of procedures and attitudes indicating the evolution of space-visual type skills